It is known, e.g. from an article by W. B. Scott published in the journal “Aviation Week and Space Technology” of Jul. 5, 1999, to arrange a plurality of small rocket engines in a ramjet. However that article remains vague about the particular design of the small rocket engines.
A major problem is cooling the walls of the combustion chambers and the nozzles of those small rocket engines, given that the temperature reached by the combustion gas is greater than 3000 K. This makes the length of life of such systems quite problematic, particularly if is desired to produce a machine that is reusable.